$A$ ray of light travelling through a rarer medium is incident at a very small angle $i$ on a glass slab,and after refraction,its velocity is reduced by $20 \%$. The angle of deviation is

$A$ container is half-filled with a liquid of refractive index $\mu$. The other half is filled with an immiscible liquid of refractive index $1.5\mu$. If the apparent depth of the container is $1.5$ times the actual depth, find $\mu$.

The back surface of a glass slab (refractive index $n$ and thickness $t$) is polished to act as a mirror,as shown in the figure. $A$ laser beam is incident on it,which is partially reflected and partially refracted at the air-glass interface. The refracted part is fully reflected at the mirror surface. $A$ pattern of discrete spots of light is observed on a screen placed perpendicular to the glass surface. The spacing between the spots on the screen is:

Obtain the relation between the real depth and apparent depth of the bottom of a tank filled with water when observed from air.

$A$ ray of light is incident normally on a glass slab of thickness $5 \ cm$ and refractive index $1.6$. The time taken by a ray to travel from the source of light to the surface of the slab is the same as the time taken to travel through the glass slab. The distance of the source from the surface is: (in $cm$)

$A$ composite slab consisting of different media is placed in front of a concave mirror of radius of curvature $150 \, cm$. The whole arrangement is placed in water (refractive index $\mu = 4/3$). An object $O$ is placed at a distance $20 \, cm$ from the slab. The refractive indices of the different media are given in the diagram. Find the final image formed by the system.